Sports Analytics R Exercises: 20 Real-World Practice Problems

Explanation: summarise() collapses the per-game rows into a single row, and naming each output column explicitly produces the same shape a scout would expect on a one-pager. If you forget round(), the output looks busier than it needs to. For a multi-stat audit on many columns, summarise(across(c(pts, reb, ast), mean)) is the scalable form.

Explanation: across() builds a matrix of logical TRUE/FALSE flags and rowSums() counts how many stat categories cleared 10. Asking >= 2 matches the textbook double-double definition. A common mistake is pts >= 10 & reb >= 10 which only flags pts-and-reb pairs and misses pts-and-ast or reb-and-ast doubles, which is what tripped up this player's recent agent during negotiations.

Explanation: TS% is a single number that beats raw FG% because it gives credit for three-pointers and free throws, which is why front offices use it for shot-creator evaluation. The 0.44 multiplier estimates how many possessions a typical free-throw trip costs (and-ones, technical FTs slightly distort the constant but 0.44 is the league convention). Always round before arrange so ties resolve by stable ordering.

Explanation: Game logs naturally store two teams per row, so a tidy standings calc almost always unpivots into a long one-row-per-team-per-game table first. bind_rows() of the home and away slices gives the cleanest unpivot here. Skipping this step and trying to sum from the wide schema usually means writing the same logic twice and double-counting ties on the boundary games.

Explanation: Sorting by two keys with arrange(desc(win_pct), desc(point_diff)) mirrors the bylaws of nearly every league: primary record, secondary differential. Note that we recompute the long table to carry both pf and pa columns; chaining off the result of 2.1 would have dropped the raw scores. Real tiebreaker chains can go five keys deep (head-to-head, division record, conference record).

Explanation: Home-court advantage is real (roughly +3 points in the NBA, more in college and European football) so isolating it lets staff target road-trip prep. The full_join() is defensive: if a team appears only on the home or only on the away side of the schedule, an inner join would silently drop it. For a real schedule you would also report game counts to flag small-sample splits.

Explanation: Head-to-head matrices are the canonical shape for playoff tiebreak displays. The pattern is: long-tidy first, then pivot_wider() for presentation. The trailing mutate(across(...)) sets the diagonal to NA so the matrix reads correctly. If two teams never met (rare in a round-robin, common in early-season cuts), pivot_wider() would emit NA there too, which is the right behavior.

Explanation: Pythagorean expectation is the cleanest one-line power rating in sports analytics: it underrates teams with extreme garbage-time stats but is robust to schedule quirks. The exponent varies by sport (baseball: ~1.83, NFL: ~2.37, NBA: ~13.91 to ~16). When actual wins lag the Pythagorean estimate by 5+, the team is usually unlucky in close games and likely to regress positively next year.

Explanation: Expected score follows a logistic curve on rating difference scaled by 400, the convention from chess. Because Team A was the underdog, beating Team B yields a bigger swing than Team B would have gained from a routine win. K controls volatility: higher K (e.g. 32) tracks form changes faster but is noisier; FiveThirtyEight uses ~20 for NBA. ELO is zero-sum game-by-game, which is why the two deltas have equal magnitude.

Explanation: End-to-end ELO is exactly the multi-step workflow analytics staff run nightly: load schedule, walk forward in date order, update ratings, post the leaderboard. Doing it in a for loop is fine for a few thousand games; for whole-league multi-decade walks you would vectorize the within-day delta or move to data.table for speed. Note that ELO sums are invariant: the league's mean rating stays at 1500.

Explanation: SoS is the key adjustment for any naive standings comparison: an 8-2 team that beat only losing teams is materially weaker than a 7-3 team that ran the gauntlet of contenders. The join key flips on purpose (opp = team) so the win_pct attached is the opponent's, not the team's own. NCAA basketball uses a more elaborate SoS that recursively folds in opponents' opponents.

Explanation: sign() collapses any number to -1, 0, or 1, and diff() != 0 flags every transition between consecutive non-zero values. Filtering out zeros first avoids counting a tie-then-recover as two changes; broadcasters typically treat a tied score as continuation of the prior lead. For a tibble of PBP rows, the same idea sits inside mutate(lead_change = sign(home_lead) != lag(sign(home_lead))).

Explanation: A two-feature logistic model is the textbook starting point for in-game win probability, and serious production models (ESPN's WPA, Inpredictable) just add timeout count, possession indicator, and team-strength priors. type = "response" returns probabilities directly; omitting it gives log-odds, which is the most common silent bug in dashboards. unname() strips the row label so the result is a clean scalar.

Explanation: Trailing windows are the standard shape for "momentum" or "form" features because they survive ties and pauses without resetting. The pattern (NA-pad, then slide) is portable: replace sum() with mean() for an average, with var() for volatility. For long streams use zoo::rollapply() or slider::slide_dbl() for a vectorized version; the explicit sapply here is fine for live game lengths (a few hundred rows).

Explanation: Per-36 inflates bench-player rate stats fairly because 21 mp at 21.4 pts is the same production rate as a 36 mp version at 36.7 pts. Per-100-possessions (often pts * 100 / poss) is the cleaner pace adjustment for teams that vary in tempo, but per-36 is the long-standing standard on Basketball-Reference player pages. Always carry minutes alongside per-36 so readers can sanity-check small samples.

Explanation: Usage is one of the most-cited metrics in NBA front-office work because it cleanly separates volume from efficiency. The team_mp / 5 factor accounts for the fact that team minutes are accumulated five-on-five; without it players who play limited minutes would show artificially low usage. Pairing usage with TS% from Exercise 1.3 produces the classic "volume vs efficiency" scouting quadrant.

Explanation: Zone-based shot charts are the bread and butter of opponent scouting; the corner three is shorter than other threes (22 feet vs 23'9") which is why league corner 3% sits 4-5 points above top-of-key 3%. Always present attempts alongside fg_pct so small-sample zones get appropriate skepticism. For production charts, layer this aggregation onto a hexbin spatial plot.

Explanation: Composite z-scores are the workhorse of pre-draft and pre-FA shortlists because they normalize stats with different units (counting vs percentage) onto a common scale. A real scouting board would weight the four components rather than sum equally (TS often gets a 2x weight in modern front offices) and would mix in defensive metrics. The order-of-operations matters: z-score first, then sum, never the reverse.

Explanation: expand_grid() is the cleanest way to spell out a Cartesian join of two factor columns, which is exactly what a 5x5 matchup map needs. Joining each side on its native column adds the per-position efficiency values, and the subtraction produces an "edge" the coaching staff can read directly. In a real game plan the next step is to filter to the top three edges and target screens that engineer those matchups.

Explanation: Rolling minutes load is the canonical workload-management feature in modern pro sports; teams pair it with sprint exposure from GPS vests and prior injury history to gate rotations. The key R idiom is group_by(player) before the rolling window, otherwise the trailing sum at player B's first game would wrongly include player A's last four. For production code prefer slider::slide_index_dbl() over hand-rolled sapply because it handles irregular game spacing.