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<div class="ac-dropdown"></div> </div> </div> <input type="submit" value="Search" tabindex="2" /> <input type="hidden" name="pid" value="" data-search-id> <input type="hidden" name="idx" value="" data-search-idx> </form> </div> </div> <style> .site_announcement { background-color: #fffea6; text-align: center; padding: .4em 0; width: 100%; } .site_announcement div { margin: 0 .3em; } .site_announcement span { white-space: nowrap; } @media only screen and (max-width: 1000px) { .site_annoucement_extra { display: none; } } </style>  <div id="inner_nav" role="navigation" aria-label="Sections on this page and/or other pages related to this page" class=" inactive suppress_inpage_nav"> <ul class="hoversmooth"> <li class="index "><a href="/about/">About Main Page</a> </li> </ul> </div><div id="content" role="main" class="index reading"> <h1>Approximate Value</h1> <div class="section_wrapper" id="all_518063722"> <div class="section_content" id="div_518063722"> <p>Created by PFR founder Doug Drinen, the <strong>Approximate Value</strong> (AV) method is an attempt to put a single number on the seasonal value of a player at any position from any year (since 1960). The way Drinen described the intent of this measurement was:</p> <p><em>"AV is not meant to be a be-all end-all metric. Football stat lines just do not come close to capturing all the contributions of a player the way they do in baseball and basketball. If one player is a 16 and another is a 14, we can't be very confident that the 16AV player actually had a better season than the 14AV player. But I am pretty confident that the collection of all players with 16AV played better, as an entire group, than the collection of all players with 14AV."</em></p> <p><em>"Essentially, AV is a substitute for --- and a significant improvement upon, in my opinion --- metrics like 'number of seasons as a starter' or 'number of times making the pro bowl' or the like. You should think of it as being essentially like those two metrics, but with interpolation in between. That is, 'number of seasons as a starter' is a reasonable starting point if you're trying to measure, say, how good a particular draft class is, or what kind of player you can expect to get with the #13 pick in the draft. But obviously some starters are better than others. Starters on good teams are, as a group, better than starters on bad teams. Starting WRs who had lots of receiving yards are, as a group, better than starting WRs who did not have many receiving yards. Starters who made the pro bowl are, as a group, better than starters who didn't, and so on. And non-starters aren't worthless, so they get some points too."</em></p> </div> </div> <div class="section_wrapper" id="all_4539841982"> <div class="section_heading assoc_4539841982" id="4539841982_sh"> <span class="section_anchor" id="4539841982_link" data-label="Weighted Career Approximate Value" data-no-inpage="1"></span><h2>Weighted Career Approximate Value</h2> </div> <div class="section_content" id="div_4539841982"> <p>At the top of every player's PFR page, you will see "Weighted Career AV" and a ranking since 1960. You can see <a href="https://www.pro-football-reference.com/leaders/career_av_career.htm">the leaderboard here</a>. This is Doug's way of balancing peak production against raw career totals. For each player, the following weighted sum of seasonal AV scores is calculated:</p> <p>100% of the player's best season, plus 95% of his 2nd-best season, plus 90% of his 3rd-best season, plus 85% of his 4th-best season, and so on...</p> <p>(<strong>Note:</strong> "Weighted Career AV" should not be confused with "<a href="https://www.pro-football-reference.com/leaders/av_career.htm">career AV</a>", which is just the unweighted sum of a player's AV scores.)</p> </div> </div> <div class="section_wrapper" id="all_8815288381"> <div class="section_heading assoc_8815288381" id="8815288381_sh"> <span class="section_anchor" id="8815288381_link" data-label="Similar Players by AV" data-no-inpage="1"></span><h2>Similar Players by AV</h2> </div> <div class="section_content" id="div_8815288381"> <p>On a player's page, you may see <a href="https://www.pro-football-reference.com/players/F/FaulMa00.htm#sim_scores::none">a table marked "Similar Players"</a>. This uses a method Doug invented to find other players who were similar in terms of the quality and shape of their AV career arcs. For each pair of players, you give them 100 "similarity points" if they both occupy three-dimensional space and breathe air. Then you subtract one similarity point for each point of difference in their best-season AVs, .95 of a similarity point for each point of difference in their second-best-season AV, .90 of a similarity point for each point of difference in their third-best-season AV, and so on.</p> </div> </div> <div class="section_wrapper" id="all_4368609661"> <div class="section_heading assoc_4368609661" id="4368609661_sh"> <span class="section_anchor" id="4368609661_link" data-label="Where to Find AV on the Site:" data-no-inpage="1"></span><h2>Where to Find AV on the Site:</h2> </div> <div class="section_content" id="div_4368609661"> <ul class="bullets"> <li>Leaderboards: <a href="https://www.pro-football-reference.com/leaders/av_single_season.htm">Single-Season</a>, <a href="https://www.pro-football-reference.com/leaders/av_career.htm">Career</a>, <a href="https://www.pro-football-reference.com/leaders/av_active.htm">Career (Active)</a>, <a href="https://www.pro-football-reference.com/leaders/av_year_by_year.htm">Year-by-Year</a>, <a href="https://www.pro-football-reference.com/leaders/career_av_career.htm">Weighted Career</a>, <a href="https://www.pro-football-reference.com/leaders/career_av_active.htm">Weighted Career (Active)</a>, & <a href="https://www.pro-football-reference.com/years/2021/leaders.htm">Yearly League</a></li> <li>Player Pages: <a href="https://www.pro-football-reference.com/players/P/PageAl00.htm#defense::none">Stat tables</a>, <a href="https://www.pro-football-reference.com/players/Y/YounSt00.htm#sim_scores::none">Similar Players</a>, leaderboard appearances, weighted career AV listing</li> <li>Franchise Pages: <a href="https://www.pro-football-reference.com/teams/">Team listing</a>, <a href="https://www.pro-football-reference.com/teams/rav/">Season index</a>, <a href="https://www.pro-football-reference.com/teams/cin/career-av.htm">franchise career register</a></li> <li><a href="https://stathead.com/football/">Stathead Football</a>: <a href="https://stathead.com/football/player-season-finder.cgi">Player Season Finder</a> (<a href="https://stathead.com/tiny/Y39Vk">example</a>)</li> </ul> </div> </div> <div class="section_wrapper" id="all_9764197961"> <div class="section_heading assoc_9764197961" id="9764197961_sh"> <span class="section_anchor" id="9764197961_link" data-label="Full Approximate Value Methodology" data-no-inpage="1"></span><h2>Full Approximate Value Methodology</h2> </div> <div class="section_content" id="div_9764197961"> <h1>Offense</h1> <p>Every team gets this many points to divvy up among its offensive players:</p> <p><strong>team_offense_points</strong> = 100 * (team offensive points per drive) / (league average offensive points per drive),</p> <p>where</p> <p>offensive points per drive = (7*(rushTD+passTD) + 3*FG) / (rushTD + passTD + turnovers + punts + FGA)</p> <h2>Offensive line</h2> <p>As a unit, the offensive line for a given team will share this many points:</p> <p><strong>team_points_for_o_line</strong> = 5 / 11 * team_offense_points</p> <p>For each offensive lineman (and fullback and tight end), we define:</p> <p>individual_points = [(games played) + 5*(games started)*(pos_multiplier)] * (all_pro_multiplier),</p> <p>where pos_multiplier = 1.2 for tackles, 1.0 for guards and centers, 0.3 for fullbacks, and 0.2 for tight ends,</p> <p>and all_pro_multiplier = 1.9 for first-team AP all-pro, 1.6 for second-team AP all-pro, and 1.3 for a pro bowler who was not first- or second-team all-pro. [NOTE: all_pro_multiplier is for tackles, guards, and centers only, not fullbacks or tight ends.]</p> <p>Finally, each individual player receives this many points:</p> <p><strong>approx_value</strong> = (individual_points) / (sum of individual_points for all players on team) * (team_points_for_o_line)</p> <h2>Skill-position players</h2> <p>Since we know the entire offensive unit will get <em>team_offense_points</em>, and we gave <em>team_points_for_o_line</em> of those to the line, we have:</p> <p><strong>team_points_for_skill_positions</strong> = team_offense_points - team_points_for_o_line</p> <p>Now we split that up into two pieces:</p> <p><strong>team_points_for_rushers</strong> = team_points_for_skill_positions * (.22) * [(team_rsh_yards / team_total_yards ) / .37 ]</p> <p>Now every individual player gets the following share:</p> <p><strong>approx_value</strong> = (rushing yards) / (team rushing yards) * team_points_for_rushers</p> <p>Finally, we give a small bonus (or impose a small penalty) to running backs who had 200 or more carries and whose yards per carry average was much higher or lower than the league average:</p> <p>bonus = .75 * [(yards per rush) - (league yards per rush by RBs)], if the player's yards per rush is better than league average.</p> <p>penalty = 2 * [(yards per rush) - (league yards per rush by RBs)], if the player's yards per rush is worse than league average.</p> <p>Note that quarterbacks, wide receivers, and anyone else who compiles rushing yards is eligible to get approximate value points at this stage.</p> <p>Now onto the passers and receivers....</p> <p><strong>team_points_for_passers</strong> = (team_points_for_skill_positions - team_points_for_rushers) * .26</p> <p>So that leaves:</p> <p><strong>team_points_for_receivers</strong> = (team_points_for_skill_positions - team_points_for_rushers) * .74</p> <p>Anyone who had a receiving yard gets this many AV points:</p> <p><strong>approx_value</strong> = (receiving yards) / (team receiving yards) * team_points_for_receivers</p> <p>And similarly for passers.</p> <p><strong>approx_value</strong> = (passing yards) / (team passing yards) * team_points_for_passers</p> <p>And, as with rushers, we add an efficiency adjustment here for passers with at least 150 pass attempts:</p> <p>bonus = .5 * [(<a href="http://www.pro-football-reference.com/about/glossary.htm#ay/a">Adjusted yards per attempt</a>) - (League average adjusted yards per attempt)], if the player's AYPA was better than league average.</p> <p>penalty = 2 * [(Adjusted yards per attempt) - (League average adjusted yards per attempt)], if the player's AYPA was worse than league average.</p> <h1>Defense</h1> <p><strong>team_defense_points</strong> = 100 * [ (1 + 2*M - M<sup>2</sup>) / (2*M) ],</p> <p>where M = (team defensive points allowed per drive) / (league average defensive points allowed per drive)</p> <p><strong>team_points_for_front_7</strong> = (2/3) * team_defense_points</p> <p><strong>team_points_for_secondary</strong> = (1/3) * team_defense_points</p> <p>Now, for all defensive players, we compute:</p> <p><strong>individual_points</strong> = [(games played) + 5*(games started) + sacks + 4*(fumble recoveries) + 4*(interceptions) + 5*(defensive TDs) + (tkl_constant)*(tackles)] + (all_pro_bonus),</p> <p>where</p> <p>tkl_constant = 0 if the year is before 1994, and otherwise, tkl_constant = .6 if the player is a defensive lineman, .3 if the player is a linebacker, and 0 of the player is a defensive back.</p> <p>all_pro_bonus = (all_pro_level)*(year_multiplier),</p> <p>where</p> <p>all_pro_level = 1.5 for first-team all-pro, 1.0 for second-team all-pro, and 0.5 for pro bowler</p> <p>year_multiplier = (year_constant) * (number_of_games_multiplier),</p> <p>where year_constant = 40 for the pre-official sack years (1960--1981) and 80 for the post-sack years (1982-present), and<br />number_of_games_multiplier = (number of games played by each team in that season) / 16</p> <p>Now, each front-seven player gets:</p> <p><strong>approx_value</strong> = [ (individual_points) / (sum of individual_points for all front-seven players on the team) ] * team_points_for_front_7</p> <p>and each defensive back gets:</p> <p><strong>approx_value</strong> = [ (individual_points) / (sum of individual_points for all defensive backs on the team) ] * team_points_for_secondary</p> <h1>Special Teams</h1> <h2>Returns</h2> <p>Every player gets one point of approx_value for each kick or punt return TD.</p> <h2>Kickers</h2> <p>At the moment, Kicking AV is based solely on field goal & extra point performance. The core stat that determines a kicker's performance is Kicking Points Above Average (PAA), which is derived by comparing a player's XP% and his FG% at various distances (0-19 yds, 20-29 yds, 30-39 yds, 40-49 yds, 50+ yds) to the league average in the same category, to determine the number of points he added above what a league-average kicker would produce in the same number of chances.</p> <p><strong>PAA_total</strong> = PAA_xp + PAA_fg1 + PAA_fg2 + PAA_fg3 + PAA_fg4 + PAA_fg5 + PAA_fg_u</p> <p>where</p> <p>PAA_xp = xpm - xpa * lg_xp_pct</p> <p>PAA_fg1 = 3 * (fgm1 - fga1 * lg_fg1_pct)</p> <p>PAA_fg2 = 3 * (fgm2 - fga2 * lg_fg2_pct)</p> <p>PAA_fg3 = 3 * (fgm3 - fga3 * lg_fg3_pct)</p> <p>PAA_fg4 = 3 * (fgm4 - fga4 * lg_fg4_pct)</p> <p>PAA_fg5 = 3 * (fgm5 - fga5 * lg_fg5_pct)</p> <p>PAA_fg_u = 3 * (fgm_u - fga_u * lg_fg_pct)</p> <p>where fgm_u and fga_u are field goals made and attempted that are unaccounted for by the distance categories. We have complete distance data going back to 1969; from 1960-1968 we have partial distances for some players. In the case of PAA from unaccounted field goals, kickers are compared to the overall league-average FG%.</p> <p>From this, we can convert PAA into Approximate Value. First, determine what share of the team's "kicking playing time" the player has received:</p> <p><strong>k_playing_time</strong> = xpa + 3 * fga</p> <p><strong>pct_team_playing_time</strong> = k_playing_time / team k_playing_time</p> <p>Determine the amount of AV the kicker would get in his playing time if he had an average PAA (prorating a league-average 3.125 figure downwards for seasons of fewer than 16 games):</p> <p><strong>avg_AV</strong> = (3.125 / 16) * team_games * pct_team_playing_time</p> <p>Then adjust up or down based on his PAA_total (dividing by 5 arbitrarily calibrates the results to match the AV scale of kickers):</p> <p><strong>raw_AV</strong> = avg_AV + (PAA_total / 5)</p> <p>The final step is to prorate this back up to 16 team games for seasons with unusual schedules:</p> <p><strong>approx_value</strong> = 16 * (raw_AV / team_games)</p> <h2>Punters</h2> <p>Right now, punting AV is determined using gross punting average and the ability to avoid blocked punts.</p> <p>Just like with kickers, the first step is determining productivity above/below average. We're using Adjusted Punt Yards, which are gross punt yards with a 13-yard penalty for blocks (the rationale being that the punter is 13 yards behind the LOS when a block occurs, but we don't assess the full 50-yard fumble/turnover penalty -- as described in <a href="http://www.amazon.com/exec/obidos/ASIN/0446514144/footbaperspe-20">The Hidden Game of Football</a> -- because the team was punting/turning the ball over anyway).</p> <p><strong>adj_punt_ypa</strong> = (punt_yds - 13 * punt_blocked) / (punt + punt_blocked)</p> <p>Then, for each league-season, compute the league's average adj_punt_ypa using individual punters' (punt + punt_blocked) totals as the weights. Then figure out how many adjusted punt yards the player added above/below the league average:</p> <p><strong>adj_punt_yds_above_avg</strong> = (punt + punt_blocked) * (adj_punt_ypa - lg_adj_punt_ypa)</p> <p>We then begin to convert adj_punt_yds_above_avg into Approximate Value. Like with kickers, we determine what share of the team's "punting playing time" the player has received:</p> <p><strong>pct_team_playing_time</strong> = (punt + punt_blocked) / (team_punt + team_punt_blocked)]</p> <p>Then calculate the amount of AV the punter would get in his playing time if he had an average adj_punt_yds_above_avg ( prorating a league-average 2.1875 figure downwards for seasons of fewer than 16 games):</p> <p><strong>avg_AV</strong> = (2.1875 / 16) * team_games * pct_team_playing_time</p> <p>Then adjust this up or down based on his adj_punt_yds_above_avg (dividing by 200 arbitrarily calibrates the results to match the AV scale of punters):</p> <p><strong>raw_AV</strong> = avg_AV + (adj_punt_yds_above_avg / 200)</p> <p>The final step is to prorate this back up to 16 team games for seasons with unusual schedules:</p> <p><strong>approx_value</strong> = 16 * (raw_AV / team_games)</p> </div> </div> <div class="section_wrapper" id="all_7212559498"> <div class="section_heading assoc_7212559498" id="7212559498_sh"> <span class="section_anchor" id="7212559498_link" data-label="Footnote" data-no-inpage="1"></span><h2>Footnote</h2> </div> <div class="section_content" id="div_7212559498"> <p>If you're interested in seeing Doug's explanatory posts as he was initially developing the metric, you can find them at these archive links: <a href="https://web.archive.org/web/20211125090607/https://www.pro-football-reference.com/blog/index6b92.html?p=465">Part 1</a> - <a href="https://web.archive.org/web/20211118071722/https://www.pro-football-reference.com/blog/index2905.html?p=466">Part 2</a> - <a href="https://web.archive.org/web/20211128205619/https://www.pro-football-reference.com/blog/index321c.html?p=509">Part 3</a> - <a href="https://web.archive.org/web/20211128130310/https://www.pro-football-reference.com/blog/index912b.html?p=510">Part 4</a></p> </div> </div>  </div> <div id="footer" role="contentinfo"> <div id="footer_header"> <ul class="bullets-inline"><li class="user logged_in">Welcome <span class="username"></span> · <a href="https://stathead.com/profile/?utm_source=pfr&utm_medium=sr_xsite&utm_campaign=2023_01_srnav_account">Your Account</a></li> <li class="user logged_in"><a class="logout" onclick="sr_auth_logout_page_elements();if(!this.href.match('redirect_uri')){this.href += '?redirect_uri='+escape(document.location.href)}" href="https://stathead.com/users/logout.cgi">Logout</a></li> <li class="user not_logged_in"><a class="login" onclick="if(!this.href.match('redirect_uri')){this.href += '&redirect_uri='+escape(document.location.href)}" href="https://stathead.com/users/login.cgi?token=1">Ad-Free Login</a></li> <li class="user not_logged_in"><a href="https://stathead.com/users/signup.cgi">Create Account</a></li> </ul> <div class="breadcrumbs">You are here: <span itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a itemprop="item" href="/"><span itemprop="name">PFR Home Page</span></a> <meta itemprop="position" content="1" /></span> > <span itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"><a itemprop="item" href="/about/"><span itemprop="name">About</span></a> <meta itemprop="position" content="2" /></span> > <strong>Approximate Value</strong></div> </div> <div id="footer_general"> <div id="site_menu" role="navigation" aria-label="complete site index"> <div class="section_heading assoc_site_menu" id="site_menu_sh"> <span class="section_anchor" id="site_menu_link" data-label="Full Site Menu" data-no-inpage="1"></span><h2>Full Site Menu</h2> <div class="section_heading_text"> <ul><li><a data-scroll href="#header">Return to Top</a></li> </ul> </div> </div> <ul> <li><a href="/players">Players</a> <div>In the News: <a title="Caleb Williams" href="/players/W/WillCa03.htm">Caleb Williams</a>, <a title="Christian McCaffrey" href="/players/M/McCaCh01.htm">Christian McCaffrey</a>, <a title="Brock Purdy" href="/players/P/PurdBr00.htm">Brock Purdy</a>, <a title="Russell Wilson" href="/players/W/WilsRu00.htm">Russell Wilson</a>, <a title="George Kittle" href="/players/K/KittGe00.htm">George Kittle</a>, <a title="Aaron Rodgers" href="/players/R/RodgAa00.htm">Aaron Rodgers</a> <a href="/players/">...</a></div> <div>Popular: <a title="Tom Brady" href="/players/B/BradTo00.htm">Tom Brady</a>, <a title="Cam Newton" href="/players/N/NewtCa00.htm">Cam Newton</a>, <a title="Aaron Donald" href="/players/D/DonaAa00.htm">Aaron Donald</a>, <a title="Russell Wilson" href="/players/W/WilsRu00.htm">Russell Wilson</a>, <a title="Aaron Rodgers" href="/players/R/RodgAa00.htm">Aaron Rodgers</a>, <a title="Odell Beckham" href="/players/B/BeckOd00.htm">Odell Beckham Jr.</a>, <a title="J.J. 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href="/teams/tam/2024.htm">Buccaneers</a>, <a href="/teams/nor/2024.htm">Saints</a>, <a href="/teams/car/2024.htm">Panthers</a></div> <div>NFC West: <a href="/teams/crd/2024.htm">Cardinals</a>, <a href="/teams/ram/2024.htm">Rams</a>, <a href="/teams/sea/2024.htm">Seahawks</a>, <a href="/teams/sfo/2024.htm">49ers</a></div> </li> <li><a href="/years/">Seasons</a> <div><a href="/years/2024/">Current Season</a>, <a href="/years/2024/games.htm">Current Season Schedule</a>, <a href="/years/2024/leaders.htm">Current Leaders</a></div><div><a href="/years/2023/">2023</a>, <a href="/years/2022/">2022</a>, <a href="/years/2021/">2021</a>, <a href="/years/2020/">2020</a>, <a href="/years/2019/">2019</a>, <a href="/years/">...</a></div> </li> <li><a href="/leaders/">NFL Leaders</a> <div><a href="/leaders/pass_yds_career.htm">Career Passing Yards</a>, <a href="/leaders/rush_td_single_season.htm">Single Season Rush TD</a>, <a href="/leaders/sacks_single_game.htm">Single Game Sacks</a> ...</div> </li> 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